filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
SplitIfs.lean | import Mathlib.Tactic.SplitIfs
example (x : Nat) (p : Prop) [Decidable p] : x = if p then x else x := by
split_ifs with h1
· rfl
· rfl
example (x y : Nat) (p : Prop) [Decidable p] (h : if p then x = y else y = x) : x = y := by
split_ifs at h
· exact h
· exact h.symm
example (x : Nat) (p q : Prop) [Decidab... |
Inverses.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Algebra.Group.Submonoid.Pointwise
/-!
# Submonoid of inverses
Given a submonoid `N` of a monoid `M`, we define the submonoid `N.leftInv` as the submonoid ... |
Power.lean | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.Int.Parity
/-!
# Results about powers in fields or... |
Terminal.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Initial and terminal objects in a category.
##... |
Alg.lean | import Mathlib
universe v u
open CategoryTheory AlgCat
set_option maxHeartbeats 10000
set_option synthInstance.maxHeartbeats 2000
variable (R : Type u) [CommRing R]
/- We test if all the coercions and `map_add` lemmas trigger correctly. -/
example (X : Type u) [Ring X] [Algebra R X] : ⇑(𝟙 (of R X)) = id := by si... |
Semisimple.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Semisimple
/-!
# Eigenspaces of semisimple linear endomorphisms
This file contains basic result... |
Regular.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Dynamics.Ergodic.Action.Basic
import Mathlib.MeasureTheory.Group.Prod
/-!
# Regular action of a group on itself is ergodic
In this file we prove th... |
Traversable.lean | import Mathlib.Tactic.DeriveTraversable
import Mathlib.Control.Traversable.Instances
set_option linter.style.commandStart false
namespace Testing
universe u
structure MyStruct (α : Type) where
y : ℤ
deriving LawfulTraversable
#guard_msgs (drop info) in #synth LawfulTraversable MyStruct
inductive Either (α : T... |
Pointwise.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Group.Bounded
import Mathlib.Analysis.Normed.Group.Uniform
import Mathlib.Topology.MetricSpace.Thickening
/-!
# P... |
imset2_finset.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Check @imset2_pair.
|
Category.lean | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jingting Wang, Wanyi He, Nailin Guan
-/
import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
import Mathlib.RingTheory.QuotSMulTop
/-!
# Categorical constructions for `IsSMulRegular`
-... |
Sublattice.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.SupClosed
/-!
# Sublattices
This file defines sublattices.
## TODO
Subsemilattices, if people care about them.
## Tags
sublattice
-/
open Func... |
extraspecial.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype bigop finset prime binomial.
From mathc... |
Cardinality.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.Data.Fintype.Pigeonhole
import Mathlib.GroupTheory.OreLocalization.Basic
import Mathlib.SetTheory.Cardinal.Arithmetic
/-!
# Cardinality of Ore localizations
This fi... |
Basic.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Multiset.FinsetOps
/-!
# Lattice structure on finite sets
T... |
GammaSpecAdjunction.lean | /-
Copyright (c) 2021 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.AlgebraicGeometry.Restrict
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Adjunction.Opposites
import Mathlib.CategoryTheory.Adjun... |
Basic.lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Yuyang Zhao
-/
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.Algebra.Notation.Pi.Defs
import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs
import M... |
Comon_.lean | /-
Copyright (c) 2023 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# Comonoid objects in a cartesian monoidal category.
The catego... |
Types.lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.ModelTheory.Satisfiability
/-!
# Type Spaces
This file defines the space of complete types over a first-order theory.
(Note that types in model theor... |
Basic.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Exact
import Mathlib.Algebra.Module.ULift
import Mathlib.LinearAlgebra.Quotient.Basic
import Mathlib.LinearAlgebra.Finsupp.LinearCombination
/-!
# Prese... |
Inversion.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee, Óscar Álvarez
-/
import Mathlib.GroupTheory.Coxeter.Length
import Mathlib.Data.List.GetD
import Mathlib.Tactic.Group
/-!
# Reflections, inversions, and inversion sequences... |
Have.lean | /-
Copyright (c) 2022 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino
-/
import Mathlib.Tactic.Have
example : Nat := by
have h : Nat
exact 5
exact h
example : Nat := by
have : Nat
· exact 5
exact this
example {a : Nat} : a =... |
Defs.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Batteries.Data.Nat.Gcd
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Algebra.Order.Sub.Basic
import Mathlib.... |
CotangentComplex.lean | import Mathlib.RingTheory.Extension.Cotangent.Basic
deprecated_module (since := "2025-05-11")
|
mxpoly.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import div fintype tupl... |
Slice.lean | /-
Copyright (c) 2021 Bhavik Mehta, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import Mathlib.Data.Fintype.Powerset
import Mathlib.Order.Antichain
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Alg... |
Basic.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Short complexes
This file defines the category `ShortComplex C` of diagrams
`X₁ ⟶ X₂ ⟶ X₃` such that the com... |
Defs.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Group.Nat.Hom
import Mathlib.Algebra.Polynomial.Basic
/-!
# Evaluating a polynomial
## Main definit... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Order.Bounds.Image
import Mathlib.Order.CompleteLattice.Basic
import Mathlib.Order.WithBot
/-!
# Galois connections, insertions and coinsertions
This... |
Monoid.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Data.Set.Function
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Algebra.Order.Monoid.Defs... |
Basic.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Data.Set.Lattice.Image
import Mathlib.Data.SetLike.Basic
/-!
# Order intervals
This file defines (nonempty) close... |
ContMDiffMFDeriv.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import Mathlib.Geometry.Manifold.MFDeriv.Tangent
import Mathlib.Geometry.Manifold.ContMDiffMap
import Mathlib.Geometry.Manifold.VectorBundle.H... |
Equiv.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Data.FunLike.Embedding
/-!
# Typeclass for a type `F` with an injective map to `A ≃ B`
This typeclass is primarily for use by isomorphisms like `MonoidEqui... |
Embedding.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Logic.Embedding.Basic
import Mathlib.Algebra.Group.Defs
/-!
# The embedding of a cancellative semigroup into itself by multiplication by a fixed element... |
fintype.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnotations eqtype.
From mathcomp Require Import ssrnat seq choice pat... |
NullSubmodule.lean | /-
Copyright (c) 2024 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
import Mathlib.Analysis.Normed.Group.Continuity
import Mathlib.Analysis.Normed.MulAction
/-!
# The null subgroup in a seminormed commutative group
For any `SeminormedAd... |
Units.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Order.Hom.Basic
import Mathlib.Order.MinMax
import Mathlib.Algebra.Group.Units.Defs
/-!
# Units in or... |
PathConnected.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Path
/-!
# Path connectedness
Continuing from `Mathlib/Topology/Path.lean`, this file defines path components and path-connected
spaces.
##... |
Estimator.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Data.List.EditDistance.Bounds
import Mathlib.Order.Estimator
/-!
# `Estimator` for Levenshtein distance.
The usual algorithm for computing Levenshtein di... |
ContinuousLinearMap.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import Mathlib.Analysis.NormedSpace.HahnBanach.SeparatingDual
import Mathlib.MeasureTheory.Integral.Bochner.Set
import Mathlib.Topology.ContinuousMap.C... |
Support.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set
import Mathlib.Algebra.Notation.Support
/-!
# Support of a function composed with a scalar action
We... |
Basic.lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.Algebra.Polynomial.Splits
import Mathlib.FieldTheory.RatFunc.AsPolynomial
import Mathlib.NumberTheory.ArithmeticFunction
import Mathlib.RingTheory.Ro... |
deriving_countable.lean | import Mathlib.Tactic.DeriveCountable
import Mathlib.Data.Countable.Basic
import Mathlib.Logic.Equiv.List
/-!
# Tests of the `Countable` deriving handler
-/
namespace Test
/-!
Structure
-/
structure S (α β : Type*) where
x : α
y : List β
deriving Countable
example : Countable (S Nat Bool) := inferInstance
/-... |
Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov, Yakov Pechersky
-/
import Mathlib.Algebra.Group.Subsemigroup.Defs
import M... |
HashCommandLinter.lean | import Lean.Elab.GuardMsgs
import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.Linter.HashCommandLinter
set_option linter.hashCommand true
section ignored_commands
-- As a consequence of https://github.com/leanprover/lean4/pull/5644, `#guard_msgs in`, even without a doc-string,
-- does not triggers the `#`-co... |
closed_field.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype generic_... |
MulAction.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Data.ENNReal.Action
import Mathlib.Topology.Algebra.UniformMulAction
import Mathlib.Topology.MetricSpace.Algebra
... |
PrimePow.lean | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Algebra.IsPrimePow
import Mathlib.Data.Nat.Factorization.Basic
import Mathlib.Data.Nat.Prime.Pow
import Mathlib.NumberTheory.Divisors
/-!
# Prime powers a... |
Basic.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison, Adam Topaz, Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplexCategory.Defs
import Mathlib.Data.Fintype.Sort
import Mathlib.Order.Category.NonemptyFinLin... |
Reverse.lean | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Polynomial.Degree.TrailingDegree
import Mathlib.Algebra.Polynomial.EraseLead
/-!
# Reverse of a univariate polynomial
The main definition is `r... |
PhragmenLindelof.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.AbsMax
import Mathlib.Analysis.Asymptotics.SuperpolynomialDecay
/-!
# Phragmen-Lindelöf principle
In this file we prove several ve... |
Lex.lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Junyan Xu
-/
import Mathlib.Algebra.Order.Group.PiLex
import Mathlib.Data.DFinsupp.Order
import Mathlib.Data.DFinsupp.NeLocus
import Mathlib.Order.WellFoundedSet
/-!
# Lexic... |
DecisionNec.lean | /-
Copyright (c) 2020 Gihan Marasingha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gihan Marasingha
-/
import Archive.MiuLanguage.Basic
import Mathlib.Data.List.Basic
import Mathlib.Data.Nat.ModEq
/-!
# Decision procedure: necessary condition
We introduce a condi... |
Triangle.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Manuel Candales
-/
import Mathlib.Geometry.Euclidean.Angle.Oriented.Affine
import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine
import Mathlib.Tactic.IntervalCases
/-... |
ssrnat.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Import PosDef.
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype.
#[export] Set Warnings "-ov... |
Polar.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Kalle Kytölä
-/
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.LinearAlgebra.SesquilinearForm
import Mathlib.Topology.Algebra.Module.WeakBilin
/-!
# Polar set
I... |
Torsion.lean | /-
Copyright (c) 2025 Yaël Dillies, Patrick Luo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Patrick Luo
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Tactic.MkIffOfInductiveProp
/-!
# Torsion-free monoids and groups
This file defines torsion-... |
Triangle.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Triangulated.Basic
import Mathlib.CategoryTheory.Triangulated.Opposite.Basic
/-!
# Triangles in the opposite category of a (pre)triangulated cate... |
Over.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Sites.CoverLifting
import Mathlib.CategoryTheory.Sites.CoverPreserving
/-! Localization
In this file, given a Grothendieck topology `J` on a cat... |
Indicator.lean | /-
Copyright (c) 2023 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Metrizable
import Mathlib.MeasureTheory.Integral.Lebesgue.DominatedConvergence
/-!
# Results about indicator functi... |
presentation.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq.
From mathcomp Require Import fintype finset fingroup morphism.
(**********************... |
Bertrand.lean | /-
Copyright (c) 2020 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Bolton Bailey
-/
import Mathlib.Data.Nat.Choose.Factorization
import Mathlib.NumberTheory.Primorial
import Mathlib.Analysis.Convex.SpecificFunctions.Basic
import Math... |
Real.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Topology.Connected.PathConnected
import Mathlib.Topology.Instances.AddCircle.Defs
import Mathlib.Topology.Instances.ZMultiples
/-!
# The additive circle ove... |
SimplicialObject.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplicialObject.Basic
import Mathlib.CategoryTheory.Idempotents.FunctorCategories
/-!
# Idempotent completeness of categories of simplicial ... |
WithTop.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Ring.Nat
import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop
/-!
# Lemma about the coercion `ℕ → WithBot ℕ`.
An orphaned lemma about castin... |
OfAssociative.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.Basic
import Mathlib.Algebra.Lie.Subalgebra
import Mathlib.Algebra.Lie.Submodule
import Mathlib.Algebra.Algebra.Subalgebra.Basic
/-!
# Lie algeb... |
Basic.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.GroupWithZero.NeZero
import Mathlib.Logic.Unique
import Mathlib.Tactic.Conv
/-!
# Groups with an adjoined z... |
Defs.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.List.Defs
import Mathlib.Tactic.Common
/-!
The type `List.Vector` represents lists with fixed length.
TODO: The API of `List.Vector` i... |
BochnerL1.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.MeasureTheory.Integral.Bochner.L1
deprecated_module (since := "2025-04-06")
|
IsomOfJ.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms
import Mathlib.FieldTheory.IsSepClosed
/-!
# Elliptic curves with same j-invariants are isomorphic
## Main results
- `W... |
all_boot.v | Require Export ssreflect.
Require Export ssrbool.
Require Export ssrfun.
Require Export eqtype.
Require Export ssrnat.
Require Export seq.
Require Export choice.
Require Export monoid.
Require Export nmodule.
Require Export path.
Require Export div.
Require Export fintype.
Require Export fingraph.
Require Export tuple.... |
Bounds.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Order.Group.OrderIso
import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
import Mathlib.Order.Bounds.OrderIso
import Mathlib.Order.Galois... |
Symmetric.lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Matrix.Block
/-!
# Symmetric matrices
This file contains the definition and basic results about symmetric matrice... |
Rat.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Order.Group.Unbundled.Abs
import Mathlib.Algebra.Order.Group.Unbundled.Basic
import Mathlib.Algebra.Ring.Rat
import Mathlib.Dat... |
Bipartite.lean | /-
Copyright (c) 2025 Mitchell Horner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Horner
-/
import Mathlib.Algebra.Notation.Indicator
import Mathlib.Combinatorics.Enumerative.DoubleCounting
import Mathlib.Combinatorics.SimpleGraph.Coloring
import Mathlib.C... |
Function.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, François Dupuis
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Order.Filter.Extr
import Mathlib.Tactic.NormNum
/-!
# Convex and concave functions
This... |
Lattice.lean | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Algebra.Order.Group.PosPart
import Mathlib.MeasureTheory.Group.Arithmetic
import Mathlib.MeasureTheory.Order.Lattice
/-!
# Measurability results on grou... |
Separation.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Separation.Hausdorff
import Mathlib.Topology.Connected.TotallyDisconnected
/-!
# Separation and (dis)connectedness properties of topologi... |
Diagonal.lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
import Mathlib.Data.Int.Cast.Basic
import Mathlib.Data.Int.Cast.Pi
import Mathlib.Data.Matrix.Defs
imp... |
Coevaluation.lean | /-
Copyright (c) 2021 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.LinearAlgebra.Contraction
/-!
# The coevaluation map on finite dimensional vector spaces
Given a finite dimensional vector space `V` over a field... |
Prod.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.LpSeminorm.Basic
import Mathlib.MeasureTheory.Measure.Prod
/-!
# ℒp spaces and products
-/
open scoped ENNReal
namespace Measur... |
SeparableClosure.lean | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.SeparableDegree
import Mathlib.FieldTheory.IsSepClosed
/-!
# Separable closure
This file contains basics about the (relative) separable closure of a fie... |
Lex.lean | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.GroupWithZero.ProdHom
import Mathlib.Algebra.Order.Group.Equiv
import Mathlib.Algebra.Order.Monoid.Lex
import Mathlib.Algebra.Order.Hom.Monoi... |
SeparableMeasure.lean | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.Function.SimpleFuncDenseLp
import Mathlib.MeasureTheory.SetAlgebra
/-!
# Separable measure
The goal of this file is to give a sufficien... |
InducedCategory.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Reid Barton
-/
import Mathlib.CategoryTheory.Functor.FullyFaithful
/-!
# Induced categories and full subcategories
Given a category `D` and a function `F : C → D `from a ... |
Imo2024Q2.lean | /-
Copyright (c) 2024 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.FieldTheory.Finite.Basic
/-!
# IMO 2024 Q2
Determine all pairs $(a,b)$ of positive integers for which there exist positive integers
$g$ and $N$ such that... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
KleinFour.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.GroupTheory.SpecificGroups.Alternating.Centralizer
import Mathlib.GroupTheory.SpecificGroups.KleinFour
import Mathlib.GroupTheory.Sylow
... |
TerminatedStable.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Translations
/-!
# Stabilisation of gcf Computations Under Termination
## Summary
We show that the continuants and co... |
test_ssrAC.v | From mathcomp Require Import all_boot ssralg.
Section Tests.
Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d).
Proof. time by rewrite orbACA. Abort.
Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d).
Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort.
Lemma ... |
ContinuousEvalConst.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Constructions
/-!
# Bundled morphisms with continuous evaluation at a point
In this file we define a typeclass
saying that `F` is a type o... |
TypeCheck.lean | import Mathlib.Tactic.TypeCheck
set_option linter.unusedTactic false
/-- A term where `inferType` returns `Prop`, but which does not type check. -/
elab "wrong" : term =>
return Lean.mkApp2 (.const ``id [.zero]) (.sort .zero) (.app (.sort .zero) (.sort .zero))
/--
info: Type
---
info: Bool
---
info: Nat
---
info: ... |
UnderlyingMap.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.LocalAtTarget
import Mathlib.AlgebraicGeometry.Morphisms.Constructors
/-!
## Properties on the underlying functions of morphisms of schemes.
This... |
quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype prim... |
EnoughProjectives.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences
/-!
# Smallness of Ext-groups from the existence of enough projectives
Let `C : Type u` be an abelian categ... |
Associator.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.GradedObject.Trifunctor
/-!
# The associator for actions of bifunctors on graded objects
Given functors `F₁₂ : C₁ ⥤ C₂ ⥤ C₁₂`, `G : C₁₂ ⥤ C₃ ⥤ C... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
GromovHausdorffRealized.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.ContinuousMap.Bounded.ArzelaAscoli
import Mathlib.Topology.ContinuousMap.Bounded.Normed
import Mathlib.Topology.MetricSpace.Gluing
impor... |
LeftRight.lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Order.Antichain
import Mathlib.Topology.ContinuousOn
/-!
# Left and right continuity
In this file we prove a few lemmas about left and right cont... |
finmodule.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
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